Critical evaluation of low-order moment expansions for the bonding energy of lattices and defects

An exact evaluation of the cohesive energy $E_{\mathrm{coh}}$ in a large number of model defect and bulk systems is used to assess the accuracy of truncated moment approximations for $E_{\mathrm{coh}}$. The results show that $E_{\mathrm{coh}}$ is characterized to within a few percent by the first four moments of the density of states, over a wide range of band fillings and electron temperatures. Comparison of several types of truncated moment approximations shows that the best results are obtained with the ‘‘maximum entropy’’ and recursion methods.